In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and...

In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and Teaching (2nd ed.)

Koch, M., Gluschke, M.: Control Charts © Springer-Verlag, Berlin Heidelberg 2010

Control Charts

Michael Koch

Michael Gluschke

2



Assuring the Quality of Test and Calibration Results - ISO/IEC 17025 – 5.9

The laboratory shall have quality control procedures for monitoring the validity of tests and calibrations undertaken.

The resulting data shall be recorded in such a way that trends are detectable and, where practicable, statistical techniques shall be applied to the reviewing of the results.

3



Assuring the Quality of Test and Calibration Results - ISO/IEC 17025 – 5.9 This monitoring shall be planned and reviewed and

may include, but not be limited to, the following: regular use of certified reference materials and/or

internal quality control using secondary reference materials;

participation in interlaboratory comparison or proficiency-testing programmes;

replicate tests or calibrations using the same or different methods;

retesting or recalibration of retained items; correlation of results for different characteristics of an

item.

4



Control Charts

Powerful, easy-to-use technique for the control of routine analyses

ISO/IEC 17025 demands use wherever practicable

It is hard to imagine quality management systems in laboratories without control chart

5



History

Introduced by Shewhart in 1931 Originally for industrial manufacturing

processes For suddenly occurring changes and for slow

but constant worsening of the quality Immediate interventions reduce the risk of

production of rejects and complaints from the clients

6



Principle Take control samples during the process Measure a quality indicator Mark the measurement in a chart with warning and

action limits

concentration

upper action limit

upper warning limit

target value

lower warning limits

lower action limits

sample-# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

7



Control Charts in Analytical Science

Assign a target value Certified value of a RM/CRM (if available) Mean of often repeated measurements of

the control sample (in most cases)

8



Control Charts in Analytical Science

Warning / action limits If data are normally distributed 95.5% of the data are in µ ± 2σ 99.7% are in µ ± 3σ

± 2s is taken as warning limits ± 3s is taken as action limit

xx

9



Action Limits

There is a probability of only (100-99.7) 0.3 % that a (correct) measurement is outside the action limits (3 out of 1000 measurements)

Therefore the process should be stopped immediately and searched for errors

10



Warning Limits

(100-95.5) 4.5% of the (correct) values are outside the warning limits.

This is not very unlikely. Therefore this is only for warning, no

immediate action required.

11



Calculation of Standard Deviation Measurements marked in the control

chart are between-batch Standard deviation should also be

between-batch Estimation from a pre-period of about

20 working days Repeatability STD too narrow limits Interlaboratory STD too wide limits

12



Limits Fitness for Purpose

Action and warning limits have to be compatible with the fitness-for-purpose demands

No blind use Limits should be adjusted to fit-for

purpose requirements

13



Out-of-control Situation 1 Suddenly deviating value, outside the action

limitsconcentration

upper action limit

upper warning limit

target value

lower warning limit

lower action limit

date

12.0

6.20

0613

.06.

2006

14.0

6.20

0615

.06.

2006

16.0

6.20

0619

.06.

2006

20.0

6.20

0621

.06.

2006

22.0

6.20

0623

.06.

2006

26.0

6.20

0627

.06.

2006

14



Out-of-control Situation 2 2 of 3 successive values outside the

warning limits concentration

upper action limit

upper warning limit

target value

lower warning limit

lower action limit

date

12.0

6.20

0613

.06.

2006

14.0

6.20

0615

.06.

2006

16.0

6.20

0619

.06.

2006

20.0

6.20

0621

.06.

2006

22.0

6.20

0623

.06.

2006

26.0

6.20

0627

.06.

2006

15



Out-of-control Situation 3 7 successive values on one side of the

central line Not so critical as 1 and 2concentration

upper action limit

upper warning limit

target value

lower warning limit

lower action limit

date

12.0

6.20

0613

.06.

2006

14.0

6.20

0615

.06.

2006

16.0

6.20

0619

.06.

2006

20.0

6.20

0621

.06.

2006

22.0

6.20

0623

.06.

2006

26.0

6.20

0627

.06.

2006

16



Out-of-control Situation 4 7 successive increasing or decreasing

values Not so critical as 1 and 2 concentration

upper action limit

upper warning limit

target value

lower warning limit

lower action limit

date

12.0

6.20

0613

.06.

2006

14.0

6.20

0615

.06.

2006

16.0

6.20

0619

.06.

2006

20.0

6.20

0621

.06.

2006

22.0

6.20

0623

.06.

2006

26.0

6.20

0627

.06.

2006

17



Advantages of Graphical Display instead of in a table

Much faster

More illustrative

Clearer

18



Different Control ChartsX-chart Synonyms are X-control chart, mean control

chart or average control chart Original Shewhart-chart with single values Mainly for precision check For trueness control synthetic samples with

known content or RM/CRM samples may be analysed

It is also possible to use calibration parameters (slope, intercept) to check the plausibility (constancy) of the calibration

19



Different Control ChartsBlank Value Chart Analysis of a sample, which can be assumed

to not contain the analyte (blank) Special form of the X-chart Information about

The contamination of reagents The state of the analytical system Contamination from environment (molecular

biology laboratories) Enter direct measurements of signals, not

calculated values

20



Different Control ChartsRecovery Rate Chart - I Reflects influence of the sample matrix Principle:

Analyse actual sample (unspiked) Spike this sample with a known amount of

analyte (ΔX) Analyse again

Recovery rate:

%100RRexpected

unspikedspiked

x

xx

21



Different Control ChartsRecovery Rate Chart - II Detects only proportional systematic

errors Constant systematic errors remain

undetected Spiked analyte might be bound

differently to the sample matrix better recovery rate for the spike

Target value: around 100%

22



Different Control ChartsRange Chart Synonyms are R-chart or Precision chart. Absolute difference between the highest and

lowest value of multiple analyses Repeatability Precision check Control chart has only upper limits

concentration

upper action limit

upper warning limit

target value

sample-# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

23



Different Control ChartsDifference Chart - I Uses difference with its sign

Analyse actual sample at the beginning of a series Analyse same sample at the end of the series

Calculate difference (2nd value – 1st value) Mark in control chart with the sign

24



Different Control ChartsDifference Chart - II

Target value: around 0 Otherwise: drift in the analyses during the

series

Appropriate for repeatability precision and drift check

25



Different Control ChartsCusum Chart - I

Highly sophisticated control chart Cusum = cumulative sum = sum of all

differences from one target value Target value is subtracted from every

control analyses and difference added to the sum of all previous differences

26



Nr. x x-TCusumT = 80 s = 2.5

-30

-20

-10

0

10

20

30

0 2 4 6 8 10 12 14 16

Different Control Charts - Cusum Chart - II

70

75

80

85

90

0 2 4 6 8 10 12 14 16

1 82 +2+22 79 -1+13 80 0+14 78 -2 -15 82 +2+16 79 -1 07 80 0 08 79 -1 -19 78 -2 -310 80 0 -311 76 -4 -712 77 -3 -1013 76 -4 -1414 76 -4 -1815 75 -5 -23

27



Different Control Charts - Cusum Chart - III

V-mask as indicator for out-of-control situation

d

Choose d and so that Very few false alarms occur when the process is

under control but An important change in the process mean is

quickly detected

-30

-20

-10

0

10

20

30

0 2 4 6 8 10 12 14 16

in control

-30

-20

-10

0

10

20

30

0 2 4 6 8 10 12 14 16

out of control

28



Different Control ChartsCusum Chart - IV

Advantages It indicates at what point the process went

out of control The average run length is shorter

Number of points that have to be plotted before a change in the process mean is detected

The size of a change in the process mean can be estimated from the average slope

29



Different Control ChartsTarget Control Charts - I

In the contrary to classical control charts of the Shewhart-type the target control charts operates with fixed quality criterions and without statistically evaluated values

The limits for this type of control charts are given by external prescribed and independent quality criterions (fitness for purpose)

30



Different Control ChartsTarget Control Charts - II

All types of classical control chart (X-chart, blank value, recovery, R-, R%-chart etc.) can be used as a target control chart

A target control chart is appropriate if: There is no normal distribution of the values from the control

sample due to persisting out of control situations (e.g. blank values)

There are not enough data available for the statistical calculation of the limits (rarely analysed parameters)

There are external prescribed limits which have to be applied to ensure the quality of analytical values

31



Different Control ChartsTarget Control Charts - III

The control samples for the target control charts are the same as for the classical control charts

The limits might be given by Requirements from legislation Standards of analytical methods and requirements for internal

quality control The (minimum) laboratory-specific precision and trueness of the

analytical value, which have to be ensured The evaluation of laboratory-internal known data of the same

sample type

32



Different Control ChartsTarget Control Charts - IV

Constructed with an upper and lower limit Pre-period is not necessary Out-of-control only, if the analytical value is

higher or lower than the respective limit Nevertheless trends in the analytical quality

should be identified and steps should be taken against them

33



Different Control ChartsTarget Control Charts - V (example)

only two limits and one out-of-control situation

8

9

10

11

12

13

14

15

16

17

16

.05

.20

03

20

.05

.20

03

21

.05

.20

03

22

.05

.20

03

27

.05

.20

03

11

.06

.20

03

13

.06

.20

03

13

.06

.20

03

16

.06

.20

03

17

.06

.20

03

18

.06

.20

03

19

.06

.20

03

24

.06

.20

03

25

.06

.20

03

26

.06

.20

03

02

.07

.20

03

08

.07

.20

03

09

.07

.20

03

10

.07

.20

03

11

.07

.20

03

15

.07

.20

03

15

.07

.20

03

16

.07

.20

03

18

.07

.20

03

Values mean upper CL upper WL lower WL lower CL mean+1s mean-1s

Ammonia RM (µmol/l) Date Value

16.05.2003 12,61

20.05.2003 12,96

21.05.2003 12,36

22.05.2003 12,66

27.05.2003 12,58

11.06.2003 11,45

13.06.2003 12,28

13.06.2003 12,28

16.06.2003 12,05

17.06.2003 12,93

18.06.2003 13,13

19.06.2003 12,79

24.06.2003 12,47

25.06.2003 12,07

26.06.2003 12,6

02.07.2003 12,37

08.07.2003 13,06

09.07.2003 13,29

10.07.2003 13,75

11.07.2003 13,88

15.07.2003 15,62 Out of Control A

15.07.2003 14,3

16.07.2003 13,01

18.07.2003 14,09

Control period

OB/O/GB

KH P 9.7. / SH 3.7.03

DB

WB v. 2.7.03

GB/S/P

DB

DB Wdhl QCl neu

O v. 2.7.

O/UW/KB v. 1.7.03

O/KB/RB QCl neu

GB/S/P

OB/O/GB

RB

O / SH v. 11.6.

WB v. 12.6.03

RB/DB

O/KB

SH v. 21.5.03

RB

UW/O/KB v. 10.6

UW/O/KB Wdh.

WB/O v. 14.5./KB v. 15.5.

Comment / Out-of-control situation / Action

DB 1,2,6

DB 10, 16, 19

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

Check

34



EXCEL-Tool for Control ChartsExcelKontrol 2.1

X-/mean-charts Blank value chart Range chart with absolute ranges

Recovery rate chart Differences chart

Range chart with relative ranges

35



Control Samples No control chart without control samples Requirements:

Must be suitable for monitoring over a longer time period

Should be representative for matrix and analyte conc. Concentration should be in the region of analytically

important values (limits!), if possible Amount must be sufficient for a longer time period Must be stable for several months No losses due to the container No changes due to taking subsamples

36



Control SamplesStandard Solutions To verify the calibration Control sample must be completely

independent from calibration solutions Influence of sample matrix cannot be

detected Limited control for precision (no matrix

effect) Very limited control for trueness

37



Control SamplesBlank Samples Samples which probably do not contain the

analyte To detect errors due to

Changes in reagents New batches of reagents Carryover errors Drift of apparatus parameters

Blank value at the start and at the end allow identification of some systematic trends

38



Control SamplesReal Samples

Multiple analyses for range and differences charts

If necessary separate charts for different matrices

Rapid precision control No trueness check

39



Control SamplesReal Samples Spiked with Analyte For recovery rate control chart Detection of matrix influence If necessary separate charts for

different matrices Substance for spiking must be

representative for the analyte in the sample (binding form!)

Limited check for trueness

40



Control SamplesSynthetic Samples

Synthetically mixed samples In very rare cases representative for

real samples If this is possible precision and

trueness check

41



Control SamplesReference Materials CRM are ideal control samples, but

Often too expensive or Not available

In-house reference materials are a good alternative Can be checked regularly against a CRM If the value is well known good possibility for

trueness check Retained sample material from interlaboratory

tests

42



Which One?

There are a lot of possibilities Which one is appropriate? How many are necessary?

The laboratory manager has to decide! But there can be assistance

43



Choice of Control Charts - I

The more frequent a specific analysis is done the more sense a control chart makes

If the analyses are always done with the same sample matrix, the sample preparation should be included. If the sample matrix varies, the control chart can be limited to the measurement only

44



Choice of Control Charts - II

Some standards or decrees (authority decisions) include obligatory measurement of control samples or multiple measurements. Then it is only a minimal additional effort to document these measurements in control charts

In some cases the daily calibration gives values (slope and/or intercept) that can be integrated into a control chart with little effort

45



Benefits of Using Control Charts

A very powerful tool for internal quality control

Changes in the quality of analyses can be detected very rapidly

Good possibility to demonstrate ones quality and proficiency to clients and auditors

In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and...

Documents

Transcript of In: Wenclawiak, Koch, Hadjicostas (eds.) Quality Assurance in Analytical Chemistry – Training and...